Cosmic time functions in certain Robinson-Trautman space-times

A class of Robinson-Trautman space-times is investigated with respect to the existence and properties of cosmic time functions and corresponding surfaces of simultaneity, partial Cauchy surfaces (PCS). The existence of an horizon-like hypersurface N generated by null curves is established. Then it is proved that in any connected PCS, intersecting N and approaching the curvature singularity in a certain way, the singularity appears as a point. Some counter examples are given when these conditions do not hold, and the relation to the problem of representing particles by means of singularities is briefly discussed. (author)